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144-52x+4x^2=82
We move all terms to the left:
144-52x+4x^2-(82)=0
We add all the numbers together, and all the variables
4x^2-52x+62=0
a = 4; b = -52; c = +62;
Δ = b2-4ac
Δ = -522-4·4·62
Δ = 1712
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1712}=\sqrt{16*107}=\sqrt{16}*\sqrt{107}=4\sqrt{107}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{107}}{2*4}=\frac{52-4\sqrt{107}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{107}}{2*4}=\frac{52+4\sqrt{107}}{8} $
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